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Hi, I think is it amazing for a 17 year old teenage to write technical blog. Keep it up!

Have you learn assembly programming? It is usually taught in 1 of the 1st year modules at University level. A normal multiplication and division may translate to more than 1 instruction for processor. For most processor, operations like XOR, left-shift, right-shift, rotation, take only 1 clock cycle. That makes it pretty fast.

I guess you have learn things like binary and hexadecimal representation in poly. Many students learn this, but they never get to use them often. I once wrote a Sudoku solver. An empty cell may have a maximum of 9 possible candidates (1 ~ 9). If I use an int[] array on each cell, it is going to consume a lot of memory for a 9x9 Sudoku game. I decided to use a 9-bits integer for each cell. Each bit indicates if a candidate is possible in this particular cell. Adding/removing possible candidates in each cell can be done using AND and OR operations.

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